MATLAB: Help with vectorizing Diag command

diagvectorize

I have an MxN matrix, which I would like to turn into an MxNxN matrix, where the elements in the second and third dimensions are a diagonal matrix. It can be done in a for loop by

for ii=1:M
  newMat(ii,:,:)=diag(oldMat(ii,:))
end

Any ideas on how to vectorize this? Thanks

Best Answer

Pre-allocate:

clear
M = 200;
N = 300;
oldMat = rand(M, N);
tic;               % ORIGINAL
for ii=1:M
  newMat(ii,:,:) = diag(oldMat(ii,:));
end
toc    % 16.71 seconds (Matlab 2009a/64, Win7, Core2Duo)
tic;                 % REPMAT
[m, n]  = size(oldMat);
idx     = permute(repmat(logical(eye(n)), [1, 1, m]), [3, 2, 1]);
nM      = idx+0;
nM(idx) = oldMat;
toc    % 1.10 sec 
clear newMat
tic;                % WITH PRE-ALLOCATION
newMat = zeros(M, N, N);  % Pre-allocate!!!
for ii=1:M
  newMat(ii,:,:) = diag(oldMat(ii,:));
end
toc    % 0.68 seconds
clear newMat
tic;                 % BSXFUN
newMat = zeros(M,N,N);
newMat(bsxfun(@plus,(1:M)', (0:N-1)*(M*N+M))) = oldMat;
toc    % 0.076 seconds

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MATLAB: How to multiply a vector with each column of a matrix most efficiently

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The newer the version you're running, the more benefit you'll see from JIT enhancements, so loops aren't as slow and generally evil as they used to be.
Methods 2 & 4 both require a lot more memory and related memory operations. Assuming the variables are large, that's a lot of overhead on top of the calculations. (Also remember that MATLAB requires contiguous memory addresses for arrays.)
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MATLAB: If a value in one matrix matches that in another matrix, how to assign the same index number

Sure you can. You can use the find function to find the index at which the 2nd and 3rd column match, and then copy the elements over.

Your code could look like this:

origMat =   [10521    -45.5    50.5;
             10522    -45.5    51.5;
             10523    -45.5    52.5];
newMat =   [0    -45.5    52.5;
            0    -45.5    52.5;
            0    -45.5    51.5;
            0    -45.5    50.5];
% Loop through the new matrix
for ii = 1:size(newMat,1)
   % Find the index location where 2nd and 3rd column match
   idxLocation = origMat(:,2)==newMat(ii,2) & ... 
                 origMat(:,3)==newMat(ii,3);  
   % If valid, set the index number (1st column) of the new matrix
   if ~isempty(idxLocation)
        newMat(ii,1) = origMat(idxLocation,1);
   end
end
format short g
newMat

This gives me

newMat =
        10523        -45.5         52.5
        10523        -45.5         52.5
        10522        -45.5         51.5
        10521        -45.5         50.5

Best Answer

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MATLAB: How to multiply a vector with each column of a matrix most efficiently

MATLAB: If a value in one matrix matches that in another matrix, how to assign the same index number

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